Model Calculation for theY0*(1405)Resonance State

The ${Y_0}^{*}\mathrm{}\left(1405\right)\mathrm{}$ resonance state is considered in terms of a multichannel potential arising from vector meson ($V$) exchange between the baryon octet ($B$) and the pseudoscalar meson octet ($P$). The interactions are assumed to follow $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry; the only symmetry breaking included is that arising from the $\mathrm{PB}$ threshold separations, due to the $P$ and $B$ mass splittings. The resonance mass corresponds to a reasonable value ($\frac{f^2}{4\pi }=1.25\mathrm{}$) for the $\mathrm{VPP}$ coupling; the width then calculated is 27 MeV, comparable with the empirical value. The unitary impurities found in this ${Y_0}^{*}\mathrm{}\left(1405\right)\mathrm{}$ state are quite small, the octet admixtures being dominant and only 15% in total intensity. The effective range calculated for the $\overline{K}N$ scattering length is not large, being of order $\frac{1}{m_V}$. The relationship between the various choices possible for the definition of the resonance energy is also discussed explicitly for this case.